If g(x)=x2+x−2 and 12gof(x)=2x2−5x+2, then which is not a possible f(x)?

12(gof)(x)=2x2−5x+2 or     12g[f(x)]=2x2−5x+2∴    {f(x)}2+{f(x)}−2=22x2−5x+2 or     f(x)2+f(x)−4x2−10x+6=0∴    f(x)=−1±1+44x2−10x+62    =−1±16x2−40x+252=−1±(4x−5)2    =2x−3 or −2x+2